3.1 CDF for continuous rvs
The CDF FX(x) for a continuous rv X with PDF fX(x) is FX(x)=Pr
Example 3.1 (CDF: continuous rv) From Example 2.3, f_Z(z) = 3 z^2\quad\text{for $0<z<1$}. The CDF is F_Z(z) = \int_{-\infty}^z 3 t^2\, dt = \int_{0}^z 3 t^2\, dt = z^3. More completely and correctly, F_Z(z) = \left\{ \begin{array}{ll} 0 & \text{for $z<0$}\\ z^3 & \text{for $0\le z \le 1$}\\ 1 & \text{for $z>1$} \end{array} \right.; see Fig. 3.1.

FIGURE 3.1: The distribution function for the variable Z